As in the flee analogy, the universe 'could' go on forever, like you said it could be universe with a universe over and over and the further you put back the most is revealed, a perfect (although there is no such thing as perfection) example of this theory would be that of fractal images.

I personally don't believe there is such a thing as infinity - as in the words the oracle from the Matrix - "Everything that has a beginning, has an end", and that too includes the universe. If the universe did begin (Big Bang?), then it is also logical to assume that it ends at some point - where that point is no-one knows, but perhaps logic has no place in this subject, perhaps the nature and shear scale of the universe is beyond our understanding.

So in conclusion, the only thing (at least in my mind) that can possibly be infinite is that which did not begin, but again the very thought of something being there which did not begin is way beyond our understanding, we cannot possibly comprehend (and believe me i've tried) something that is there and always has been and was never created.

P.S. If the universe (as we know it) is expanding - then what is it expanding into, i mean - if the universe is EVERYTHING then that would seem to suggest that there would be nothing left for it to expand into...

...also assuming that the universe did 'begin' its 'life' (the universe being all that there is and was without exception)as a few 'dust' particles then:-

1. Where did these particles come from?

...and

2. Where were the particles, they must have been somewhere otherwise they would not have existed. You cannot put something into nothing. But lets just assume for a second that that was the universe that they were in (i have quite literally just thought of this), so the universe was already there minus all matter - so like a blank canvas before the moment of creation, which could possibly mean that the universe before all matter already existed. If therefore (i know this is contradictory) the universe was already there and so never created, then that would suggest that it does not have a beginning and therefore by my own logic would mean that it does not have an end and so... would - by all reasonable thought be - infinite... wow. So it wouldn't be the universe that is expanding but matter that is expanding within it.

.... and breathe. :)

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I think Bourbaki school of mathematcians had done some work to try and prove that mathematics including calculus can be developed with assuming infinity

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I think Bourbaki school of mathematcians had done some work to try and prove that mathematics including calculus can be developed withOUT assuming infinity

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